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Theorem imaeq2d 4851
Description: Equality theorem for image. (Contributed by FL, 15-Dec-2006.)
Hypothesis
Ref Expression
imaeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
imaeq2d  |-  ( ph  ->  ( C " A
)  =  ( C
" B ) )

Proof of Theorem imaeq2d
StepHypRef Expression
1 imaeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 imaeq2 4847 . 2  |-  ( A  =  B  ->  ( C " A )  =  ( C " B
) )
31, 2syl 14 1  |-  ( ph  ->  ( C " A
)  =  ( C
" B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1316   "cima 4512
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-3an 949  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-sn 3503  df-pr 3504  df-op 3506  df-br 3900  df-opab 3960  df-xp 4515  df-cnv 4517  df-dm 4519  df-rn 4520  df-res 4521  df-ima 4522
This theorem is referenced by:  imaeq12d  4852  nfimad  4860  elimasng  4877  ressn  5049  foima  5320  f1imacnv  5352  fvco2  5458  fsn2  5562  resfunexg  5609  funfvima3  5619  funiunfvdm  5632  isoselem  5689  fnexALT  5979  eceq1  6432  uniqs2  6457  ecinxp  6472  mapsn  6552  phplem4  6717  phplem4dom  6724  phplem4on  6729  sbthlem2  6814  isbth  6823  resunimafz0  10542  ennnfonelemg  11843  ennnfonelemhf1o  11853  ennnfonelemex  11854  ennnfonelemrn  11859  cnntr  12321  cnptopresti  12334  cnptoprest  12335
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